ABCD, E is the midpoint of DC & F is the midpoint of AB. If FE=9 what is the length of diagonal AC?

Question

Okay so there is a maximum on the thing it is a parallelogram I couldn't write it because I was over the max. Doing extra credit and using a parallelogram which is aactually kinda like 2 parallelograms (if you wanted to make sure if you drew it right) just someone please help IDK what to do!

Answer 1

So AD=FE=BC=9 and AB=DC. More info is needed! Let's say AB=a, a known quantity. We also need an angle. Let's pick A=x, another known quantity. The other angles will be: B=180-x=D and C=x. By the cosine rule, in triangle ACD, AC^2=AD^2+DC^2-2AD.DCcosD. So AC^2=81+a^2-18acos(180-x)=81+a^2+18acosx. AC=sqrt(81+a^2+18acosx).

Put x=60° and a=18, then AC=sqrt(81+324+162)=sqrt(567)=9sqrt(7)=23.81.